ORBi Collection: Mathematics
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LaTeX, un peu, beaucoup (2. L'aspect terre-à-terre de la question)
http://hdl.handle.net/2268/170451
Title: LaTeX, un peu, beaucoup (2. L'aspect terre-à-terre de la question)
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<br/>Author, co-author: Dupont, Pascal; Henry, Valérie; Sebille, MichelFri, 11 Jul 2014 17:10:39 GMTThe number of structures compatible with any given correlation function
http://hdl.handle.net/2268/170357
Title: The number of structures compatible with any given correlation function
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<br/>Author, co-author: Gommes, CédricWed, 09 Jul 2014 14:36:20 GMTIdentifying codes in vertex-transitive graphs
http://hdl.handle.net/2268/170304
Title: Identifying codes in vertex-transitive graphs
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<br/>Author, co-author: Gravier, Sylvain; Parreau, Aline; Rottey, Sara; Storme, Leo; Vandomme, Elise
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<br/>Abstract: We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the optimal integer and fractional solutions is between 1 and 2 log(|V|) where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that reach both bounds. We exhibit infinite families of vertex-transitive graphs with integer and fractional identifying codes of order |V|^a with a in {1/4, 1/3, 2/5}. These families are generalized quadrangles (strongly regular graphs based on finite geometries). They also provide examples for metric dimension of graphs.Wed, 09 Jul 2014 10:26:46 GMTLaTeX, un peu, beaucoup (4. Les "équations" et leurs styles)
http://hdl.handle.net/2268/170300
Title: LaTeX, un peu, beaucoup (4. Les "équations" et leurs styles)
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<br/>Author, co-author: Dupont, PascalWed, 09 Jul 2014 10:04:58 GMTLaTeX, un peu, beaucoup (3. Le béhaba)
http://hdl.handle.net/2268/170297
Title: LaTeX, un peu, beaucoup (3. Le béhaba)
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<br/>Author, co-author: Dupont, PascalWed, 09 Jul 2014 09:57:28 GMTSur les quantifications équivariantes en supergéométrie de contact
http://hdl.handle.net/2268/169770
Title: Sur les quantifications équivariantes en supergéométrie de contact
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<br/>Author, co-author: Nibirantiza, AboubacarTue, 01 Jul 2014 14:37:04 GMTHigher Symmetries of the conformal Laplacian
http://hdl.handle.net/2268/169171
Title: Higher Symmetries of the conformal Laplacian
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<br/>Author, co-author: Radoux, FabianMon, 16 Jun 2014 12:30:13 GMTLongitudinal quality of life data: a comparison of continuous and ordinal approaches
http://hdl.handle.net/2268/168899
Title: Longitudinal quality of life data: a comparison of continuous and ordinal approaches
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<br/>Author, co-author: Donneau, Anne-Françoise; Mauer, Murielle; Coens, C; Bottomley, A; Albert, AdelinTue, 10 Jun 2014 07:53:34 GMTFree Group and Recognizability
http://hdl.handle.net/2268/168800
Title: Free Group and Recognizability
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<br/>Author, co-author: Raskin, Julien
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<br/>Abstract: It is well known that recognizability has many algebraic properties. For example, a subset $L$ of the free monoid $\Sigma^*$ is recognizable if and only if there exists a finite monoid $M$, a subset $P$ of $M$ and a morphism $f : \Sigma^* \to M$ such that $L = f^{-1}(P)$. These properties allow us to easily define a concept of recognizability in non-free monoids or even in other algebraic structures, such as groups.
Our aim is to study the recognizable subsets of the free group $F_X$ generated by $X$. A classical construction of the latter shows that it can be seen as a subset of the free monoid $(X \cup X')^*$, where $X'$ is a set of formal inverses of elements of $X$, endowed with an ad hoc operation. When $X$ is finite, it appears that $F_X$ is a recognizable language of this monoid. It is then natural to wonder if there is a link between recognizability in $F_X$ and recognizability in $(X \cup X')^*$. We show that every recognizable language of $F_X$ is recognizable in $(X \cup X')^*$, and that we can define a class of automata that recognize the recognizable languages of $F_X$.Fri, 06 Jun 2014 15:17:34 GMTParametric conditional variance estimation in location-scale models with censored data
http://hdl.handle.net/2268/168767
Title: Parametric conditional variance estimation in location-scale models with censored data
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<br/>Author, co-author: Heuchenne, Cédric; Laurent, Géraldine
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<br/>Abstract: Suppose the random vector (X,Y) satisfies the regression model Y=m(X)+sigma(X)*varepsilon,
where m(.)=E(Y|.), sigma²(.)=Var(Y|.) belongs to some parametric class {sigma _theta(.): theta in Theta} and varepsilon is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. A new estimation procedure is proposed for sigma_theta(.) when m(.) is unknown. It is based
on nonlinear least squares estimation extended to conditional variance in the censored case. The consistency and asymptotic normality of the proposed estimator are established. The estimator is studied via simulations
and an important application is devoted to fatigue life data analysis.Fri, 06 Jun 2014 06:01:39 GMTEstimation of the error distribution in nonparametric regression with cross-sectional data
http://hdl.handle.net/2268/168752
Title: Estimation of the error distribution in nonparametric regression with cross-sectional data
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<br/>Author, co-author: Heuchenne, Cédric; Laurent, Géraldine
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<br/>Abstract: In this article, we study the nonparametric regression model Y=m(X)+varepsilon where m(x)=E[Y|X=x] and sigma²(x)=Var[varepsilon|X=x] are unknown smooth functions, and the error varepsilon has zero mean and finite variance conditionally on X=x. The problem consists in estimating the cumulative distribution function of the error in a nonparametric way when the couple (X,Y) is obtained by cross-sectional sampling while the positive response Y can be right-censored. We propose a new estimator for the error distribution function based on the estimators of m(.) and sigma²(.) described in Heuchenne and Laurent 2014. A bootstrap procedure is developed to solve the critical problem of the smoothing parameter choice. We assess the performance of the proposed estimator through simulations. Finally, a data set based on the mortality of diabetics is analyzed. (Heuchenne Cédric and Laurent Géraldine, Nonparametric regression with cross-sectional data: an alternative to conditional product-limit estimators, 2014)Thu, 05 Jun 2014 14:27:49 GMTFrom censored to cross-sectional data: non and semiparametric new developments
http://hdl.handle.net/2268/168751
Title: From censored to cross-sectional data: non and semiparametric new developments
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<br/>Author, co-author: Laurent, Géraldine
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<br/>Abstract: In many statistical studies, an observation is evident: the available data are regularly right-censored. A censorship arises when, for different reasons, the data time of interest can not be observed. A data is so right-censored if, instead of observing its time of interest, a lower bound of this time is considered for this data. For example, the study duration can be shorter than the time of interest leading then to a correspondence between the observed times and the study end time. Moreover, these data can be obtained from cross-sectional process. Cross-sectional process selects only data in progress at a fixed time to constitute the studied sample, determining the data followed for the study. Therefore, cross-sectional process introduces left truncation. A data is described as left-truncated if its time of interest is larger or equal to a fixed time.
It is in this context this thesis has been elaborated. The considered estimation problems for such data will be studied with a nonparametric or semiparametric approach. An approach is nonparametric or semiparametric if none assumption is supposed about the belonging to parametric family for the time of interest distribution function, solely based on qualitative hypotheses. These estimation methods have thus the advantage to be based on weaker assumptions in comparison with the parametric approaches. The aim of the different researches developed in this thesis is to improve the current estimation techniques.
This thesis is organised in four parts.
The first part (first chapter) determines the context of our researches through practical examples and a significant but not exhaustive literature overview as well as our motivation about the different researches presented in this thesis. To conclude this first part, our contributions in these researches are briefly explained.
The second part (second chapter) presents a new estimation procedure for the parameters of the parametric conditional variance in the heteroscedastic regression situation applied to right-censored data. This procedure constructs artificial data to replace censored data exploiting a heteroscedastic regression model and then defines the optimal parameters from the least squares method. The interest of this research is to fill a gap in the current literature.
The third part (third and fourth chapters) studies, in a regression context, the cross-sectional data, i.e. left-truncated and right-censored data, where the conditional truncation distribution function is supposed to be known. The innovation of the method proposed here consists in the use of information contained in the conditional truncation distribution function for the nonparametric estimation methods.
Finally, the fourth part (fifth chapter) is devoted to the cross-sectional data examination but this time for nonparametric estimation of the time of interest distribution function. In this chapter, the truncation distribution function is supposed to belong to a parametric family and not known anymore. The relevance of this approach is due to this weaker assumption than one in the above part. This information about the truncation distribution function is also introduced in the nonparametric estimation.
This thesis concludes with a set of suggestions related to possible future researches in these statistical fields.Thu, 05 Jun 2014 14:17:49 GMTEstimation from cross-sectional data under a semiparametric truncation model
http://hdl.handle.net/2268/168750
Title: Estimation from cross-sectional data under a semiparametric truncation model
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<br/>Author, co-author: de Uña-Álvarez, Jacobo; Heuchenne, Cédric; Laurent, Géraldine
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<br/>Abstract: Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family, while nothing is assumed on lifetime and censoring distributions. The novelty of this work is in the fact that it introduces estimators of this semiparametric model in the presence of censoring. Two alternative methods are considered, based on conditional and full likelihood considerations. Asymptotic representations of the estimators for the lifetime distribution are obtained, and their weak convergence is established. The finite sample performance of the new estimators is explored through simulations, and two real data illustrations are provided. One of the conclusions of our research is that both estimators perform better than Wang's NPMLE
when the parametric family for the truncation variable is valid) in the sense of the integrated mean squared error, and that the full likelihood approach is preferable to the conditional likelihood approach for the estimation of the lifetime distribution but not necessarily for the estimation of the truncation distribution.Thu, 05 Jun 2014 14:09:55 GMTNonparametric regression with cross-sectional data: an alternative to conditional product-limit estimators
http://hdl.handle.net/2268/168749
Title: Nonparametric regression with cross-sectional data: an alternative to conditional product-limit estimators
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<br/>Author, co-author: Heuchenne, Cédric; Laurent, Géraldine
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<br/>Abstract: Suppose the random vector (X,Y) satisfies the nonparametric regression model Y=m(X)+varepsilon, where m(x)=E[Y|X=x] and sigma²(x)=Var[varepsilon|X=x] are unknown smooth functions and the error varepsilon has zero mean and finite variance conditionally on X=x. The pair (X,Y) is obtained by cross-sectional sampling involving left-truncated and right-censored responses. The considered model is completely nonparametric but the conditional truncation distribution is assumed to be known. The novelty of this work is twofold: first, it extends the results on cross-sectional data to the conditional case and second, it generalizes the length bias results in the conditional case to right censoring and to any truncation distribution. New estimators for m(.) and sigma²(.) are constructed and relevant tools are used to quickly provide the main asymptotic properties for this kind of estimators.
Extensive simulations are carried out and show that the new estimators outperform classical nonparametric estimators for left-truncated and right-censored data (when the truncation model is known). Finally, a data set on the mortality of diabetics is analyzed.Thu, 05 Jun 2014 13:59:06 GMTMultivariate coefficients of variation: comparison and influence functions
http://hdl.handle.net/2268/168736
Title: Multivariate coefficients of variation: comparison and influence functions
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<br/>Author, co-author: Aerts, Stéphanie; Haesbroeck, Gentiane; Ruwet, Christel
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<br/>Abstract: In the univariate setting, coefficients of variation are well known and used to compare the variability of populations characterized by variables expressed in different units or having really different means. When dealing with more than one variable, the use of such a relative dispersion measure is much less common even though several generalizations of the coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, the lack of robustness of the sample versions of the multivariate CV's is illustrated by means of influence functions and a robust counterpart based on the Minimum Covariance Determinant (MCD) estimator is advocated. Then, focusing on two of the considered multivariate CV's, a diagnostic tool based on their influence functions is derived and its efficiency in detecting observations having an unduly large effect on variability is illustrated on a real-life data set. The influence functions are also used to compute asymptotic variances under elliptical distributions, yielding approximate confidence intervals. Finally, simulations are conducted in order to compare the performance of the classical and robust multivariate CV's in a finite sample setting. As expected, when the data are normally distributed, the classical estimator performs better than the robust counterpart based on the MCD estimator, while the reverse is true when the data are contaminated.Thu, 05 Jun 2014 08:37:31 GMTMultifractal analysis of air temperature signals using the wavelet leaders method
http://hdl.handle.net/2268/168669
Title: Multifractal analysis of air temperature signals using the wavelet leaders method
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: We use the discrete "wavelet transform microscope" to show that the surface air temperature signals of weather stations selected in Europe are monofractal. This study reveals that the information obtained in this way are richer than previous works studying long range correlations in meteorological stations. The approach presented here allows to bind the Hölder exponents with the climate variability. We also establish that such a link does not exist with methods previously carried out, such as the detrended fluctuation analysis.Mon, 02 Jun 2014 16:41:08 GMTDistribution under elliptical symmetry of a distance-based multivariate coefficient of variation
http://hdl.handle.net/2268/168628
Title: Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation
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<br/>Author, co-author: Aerts, Stéphanie; Haesbroeck, Gentiane; Ruwet, Christel
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<br/>Commentary: In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable to its mean. It is particularly recommended when comparing populations with significantly different means. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on one particular extension based on the Mahalanobis distance between the mean and the origin of the design space and suggest to estimate that quantity by plugging the empirical mean and covariance matrix in its definition. The distribution of this sample estimator is analyzed under elliptical distributions and used, under normality, to build exact confidence intervals. As the natural estimator is biased, two bias reduction techniques are constructed and compared by means of simulations. Some real examples are discussed throughout the sequel to motivate the use of the considered multivariate relative dispersion measure.Mon, 02 Jun 2014 09:33:48 GMTAngles corniculaires et de demi-cercle chez Euclide
http://hdl.handle.net/2268/168434
Title: Angles corniculaires et de demi-cercle chez Euclide
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<br/>Author, co-author: Bair, Jacques; Henry, Valérie
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<br/>Abstract: Les angles datent de l’Antiquité : ils sont présents dans le célèbre ouvrage "Les Éléments" d’Euclide. En partant des "Commentaires" de Proclus, nous présentons la façon dont Euclide introduisait le concept d'angle et sa distinction entre les angles rectilignes et mixtilignes. Les cas des angles corniculaires et de demi-cercle sont spécialement traités.Tue, 27 May 2014 12:14:48 GMTTour d’horizon sur des algèbres généralisant les octonions
http://hdl.handle.net/2268/168385
Title: Tour d’horizon sur des algèbres généralisant les octonions
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<br/>Author, co-author: Kreusch, Marie
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<br/>Abstract: Une nouvelle série d'algèbres réelles généralisant l'algèbre des octonions, tout comme les algèbres de Clifford prolongent l'algèbre des quaternions, a été introduite par Morier-Genoud $\&$ Ovsienko en 2011. Ces algèbres, qui ne sont ni commutative, ni associative, peuvent être vues comme des algèbres twistées sur le groupe $(\mathbb{Z}_2)^n$ avec une fonction de twist cubique.
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Les propriétés de périodicités de ces algèbres sont similaires à celles déjà bien connues sur les algèbres de Clifford. Ce résultat donnera lieu à une discussion sur les formes cubiques définies sur $(\mathbb{Z}_2)^n$ à valeurs dans $\mathbb{Z}_2$.Mon, 26 May 2014 10:06:17 GMTSpline approximation to conditional Archimedean copula
http://hdl.handle.net/2268/168352
Title: Spline approximation to conditional Archimedean copula
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<br/>Author, co-author: Lambert, Philippe
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<br/>Abstract: We propose a flexible copula model to describe changes with a covariate in the dependence structure of (conditionally exchangeable) random variables. The starting point is a spline approximation to the generator of an Archimedean copula. Changes in the dependence structure with a covariate x are modelled by flexible regression of the spline coefficients on x. The performances and properties of the spline estimate of the reference generator and the abilities of these conditional models to approximate conditional copulas are studied through extensive simulations. Inference is made using Bayesian arguments with posterior distributions explored using importance sampling or adaptive MCMC algorithms. The modelling strategy is illustrated with the analysis of bivariate growth curve data.Sat, 24 May 2014 08:51:41 GMT